(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

how many real variables would be required to construct a most general 2by2 unitary matrix?

2. Relevant equations

a unitary matrix U is one for which the U(U hermitian) = identity matrix or (U hermitian)U = identity matrix

3. The attempt at a solution

first i wrote the unitary matrix as {{a1+ib1,a2+ib2},{a3+ib3,a4+ib4}}, where 'i' is square root of -1. using the condition U(U hermitian) = identity matrix, i get four independent equations. thus, i should expect the number of real variables required as 8 - 4 (number of constraints) = 4. but if i consider the definition (U hermitian)U = identity matrix, i get another set of four equations. Does that mean that the number of real variables required is 8-8 =0?

there is another way to attack the problem. a hermitian matrix must have real diagonal elements. the (1,2) element must be the complex conjugate of the (2,1) element and hence, i need 4 real variables to construct the most general 2by2 hermitian matrix. since a unitary matrix can be written as exp(iH) where H is a hermitian matrix, does this also indicate that i would need 4 variables for a unitary matrix as well?

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# Homework Help: Number of real variables required to construct the most general 2by2 unitary matrix

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